This quotient construction is defined in Section REF  below. For completeness, we include the following material from Section 6 of [1]}.
The 2-form on the double \(D(G)\)  is given in [1]}:
\( \omega _D \,=\, \frac{1}{2} (a^* \theta , \,b^* \overline{\theta }) + \frac{1}{2} (a^* \overline{\theta },\, b^* {\theta }), \) 
